1

Social Networks and College Performance:

Evidence from Dining Data

Darius Martin

Adam Wright

John M. Krieg

Department of Economics

Western Washington University

Bellingham, WA 98225, USA

March 2020

Abstract

We investigate the effect of friends in class on academic performance in college using

unique data on dining card swipes at a medium-sized public university. We define

friendships by academic quarter as repeated meetings among students in the same

dining hall. To identify the impact of having a friend in class, we employ models with

student- and class-level fixed effects as well as a number of controls to rule out

alternative explanations for our findings. We find that having a friend in class has a

large and positive effect on grades, and these results are robust to wide range of

friendship criteria and econometric specifications. In line with previous evidence on

peer effects, we find that the friendship effect varies by the friends’ observable

characteristics and the strength of the friendship.

JEL Classification: I21

Keywords: Friend effects, Peer effects, Social networks

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1 Introduction

Peer interactions have long been argued to play a significant role in academic

achievement. It has been established that peers influence a wide range of outcomes including test

scores, major choice, and academic grades as well as outcomes and behaviors that indirectly

impact human capital accumulation like health and risk-taking behaviors.1 Due to data

limitations, most studies proxy for social interaction using a peer group defined at an aggregated

level such as a neighborhood, school, grade, class, or residence hall. Designating peer groups in

this manner, however, does not incorporate information on who students interact with nor does it

account for the strength of those interactions. Recent work has begun to shed light on the

importance of strong social ties, or friendships, for academic outcomes though much remains

unexplained.2 In particular, the effect of friends during post-secondary education, a time in which

new friend groups are being formed and important decisions regarding human capital

accumulation are being made, has yet to be explored.

In this paper, we analyze the effect of social networks on academic performance at the

beginning of college. Our contribution is to assess the impact of having peers with strong social

ties, or “friends”, in the same college courses while carefully addressing the nature of friendship

formation and course selection. In the economics of education literature, friendship data is quite

limited – most studies rely on the National Longitudinal Study of Adolescent Youth (Add

Health) survey in which high school respondents are able to self-nominate up to five friends of

each gender.3 Using this data to identify social networks has three shortcomings: 1) for a given

1 See Sacerdote (2011), Sacerdote (2014), and Epple and Romano (2011) for a review of this literature. 2 See for example Pattacchini, et al. (2017), Lavy and Sand (2018), and Lam (2012). 3 The main draw of using Add Health data is that it contains a nationally representative sample of high school

students who are surveyed on a number of typical demographic and outcome variables as well as friendship

questions. See for example Fletcher et al. (2020), Bramoullé et al. (2009), Lin (2010), Pattacchini, et al. (2011), and

Pattacchini, et al. (2017).

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respondent, nominated friendships may entail varying degrees of social interaction that are

unobserved to the researcher; 2) the definition of friendship may vary across respondents

resulting in friendships of different strengths being measured by the researcher as similar; and 3)

respondents may not mutually identify each other as friends leaving researchers to speculate on

the nature of relationships between these pairs.

We circumvent many of these problems by using a revealed-preference identifier of

friendships. Specifically, we leverage data from university dining halls to identify pairs of

students who regularly dine together. Since the vast majority of freshmen frequently enter the

university dining halls, we can construct quite detailed information about each freshman’s

dining-related social network. Moreover, assuming that people dine more often with better

friends, this data enables us to distinguish between stronger and weaker friendships. We validate

our friendship measure by showing that assigned friendship dyads are significantly more likely

to exhibit homophily than random pairings of dining hall users. Compared to studies that rely on

friendship nomination, like the Add Health survey, measuring friendships in this way provides

the distinct advantage that friendships and friendship-intensity are revealed rather than simply

stated.

To simplify later discussion, it is important to understand that the term “friendship” as

used in this paper represents a symmetric, binary relation between pairs of students who are

observed meeting in a dining hall with sufficient frequency. Of course, this differs from the

broader social definition of friendship commonly used. We select designating criteria such that if

two students are described as friends in this paper, then the social relationship as more broadly

understood almost certainly holds between them. That is, under strict enough social interaction

criteria, our friendship-determination method is likely a sufficient condition for identifying

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friendships. Note, however, that it is not a necessary condition for the social relationship; two

students may share a strong social bond despite not being identified as friends using our method.

We discuss the implications of this later in the paper.

Combining dining data with transcript-level data on student performance, we examine the

academic outcomes of a friendship dyad enrolling in the same course within a quarter. Though

we concentrate on friends who attend a course together in the same classroom, we expand our

analysis to include friends across sections of the same course taught by the same instructor and

by a different instructor.4 Identifying the causal effect of having friends in class on academic

performance is a difficult empirical problem because friends and classes are not randomly

assigned; students with friends may be fundamentally different from those without friends or

students may select into easier (or harder) classes based upon the presence of a friend in that

class. To mitigate these concerns, we use a within-student and within-class approach that

compares a student’s performance relative to classmates in classes taken with friends to their

relative performance in classes without friends present.

While this approach has the benefit of controlling for student- and class-level

unobservables, it does not address two other potential problems, namely correlated effects and

simultaneity. For instance, an unobserved factor that varies within students and across classes,

such as subject-specific enthusiasm, may be correlated with having friends in a class and

academic achievement (correlated effects). Alternatively, students may be more likely to make

friends in classes they find particularly easy (simultaneity). We address the issue of correlated

effects by controlling for a student’s stated interest in a subject (indicated on their application for

4 Here and throughout the paper, we use the terms “class” or “classroom” to describe a section of a course with a

specific instructor during a quarter. For example, “ECON 206: Principles of Microeconomics, Section 1” in Fall

2016. Thus, a class is a course-by-section-by-quarter.

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admission), implied subject interest given by the number of credits completed in each academic

department, and examining the effect of friends across instructors in the same course, where the

results should be qualitatively similar if shared enthusiasm is driving an observed friend effect.

The issue of simultaneity is addressed by leveraging the timing of friendships: friendships

formed in prior quarters, which cannot be affected by future grades, are used in an alternative

specification in place of contemporaneous friendships.

Our main results demonstrate a very large and robust effect of social networks on college

performance. Using many alternative criteria in designating friendships, we estimate a roughly

0.12 grade point increase (equivalent to 0.12 standard deviations) when students have a friend in

the same class, an effect size equal to an increase of a student’s Scholastic Aptitude Test (SAT)

score of about 100 points. In terms of movements in the letter grade distribution, having a friend

in class increases the probability of receiving an A grade by about 10% and decreases the

probability a D or F grade by roughly 25%.

Additionally, we are able to test how these academic improvements vary by friendship

and class characteristics. First, we find that the effect of friends increase in the “strength” of the

friendship measured by repeated social interaction both within and across academic quarters:

within a quarter, the friend effect increases with dining hall meetings and across quarters we find

that persistent friendships produce larger friend effects, consistent with recent work on short-

lived versus long-lived friendship ties.5 Second, we find many interesting patterns of

heterogeneity based on the interaction of student and friend characteristics. Students benefit less

from having a friend with a low SAT score (defined as scoring in the bottom 25th percentile),

particularly so if the students’ own SAT is low. First generation students experience increased

5 Using the Add Health survey, Patacchini, et al. (2017) show that educational outcomes are affected by long-lived

(at least one year) friendships but not short-lived (less than one year) ones.

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gains when having a friend who is not first generation. Men on average experience a larger

friend effect than women, but the friends’ gender has no differential impact on this estimate.

Lastly, friends appear to have a greater positive impact in large classes (i.e., when enrollment is

45 students or greater) but are no more effective at improving grades in hard classes (i.e., classes

where the average GPA of students without friends in class is less than 2.9).

This research is closely related to a growing body of evidence identifying the importance

of quantity and quality of friends in determining educational achievement and attainment. In

general, relatively few studies distinguish between the broader category of peers and the

narrower one of friends. The majority of these studies use the aforementioned friendship

nomination procedure among high school students in the Add Health data and generally find that

friends with better observable characteristics improve own academic outcomes.6 Lavy and Sand

(2018) exploit conditional random assignment of students to classes within Tel Aviv middle

schools to examine the impact of having pre-determined friends in class. They find the number

of friends in class has either a positive or negative effect on academic performance depending on

friends’ characteristics and the nature of the friendship. Using survey in Chinese junior high

schools, Lam (2012) is able to distinguish between friends, study mates, emotional supporters,

and seatmates and finds that positive personality traits of friends, but not their cognitive traits,

positively affect math scores.

None of this literature examines college-aged individuals, where the nature and impact of

friendships may be different from those in primary or secondary school. A number of studies

6 Using a difference-in-differences approach, Fletcher et al. (2020) find that more friends with college-educated

mothers raises high school GPA for girls but not boys. Exploiting the different waves of Add Health and using

indirect friends as an instrument for own friends, Patacchini et al. (2017) show that educational choices of long-lived

friendships (lasting more than one year) have a positive effect on own educational attainment. Hill (2015) also uses

an instrumental variables approach to demonstrate that a student’s share of opposite gender friends negatively

affects high school GPA. Bramoullé et al. (2009) and Lin (2010) show that both friends’ average grades and average

characteristics affect students’ educational attainment.

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have investigated the impact of peers at the college level, but to our knowledge, none has directly

assessed the impact of friends. Many studies use the random assignment of students to

dormitories to estimate peer effects and generally find that better peers positively influence

academic and social outcomes.7 Though, looking at college roommates or dormmates may not

provide a comprehensive view of students’ peer interactions. Carrell et al. (2009) rely on the

random assignment of students from the U.S. Air Force Academy to squadrons (i.e., cohorts),

which arguably captures a more complete group for peer interactions, and find better peers

positively influence GPA. However, findings from the Air Force may not be generalizable to

other university settings.

This study makes three novel contributions to this literature. First, we use a revealed-

preference methodology to identify friendships. This allows us to differentiate between stronger

and weaker friendships based on how often students coordinate their meals. Coordination entails

some cost to students as compared to costlessly nominating friends in a survey setting. Second,

we apply the analysis of friendships to a university setting, where students are likely forming

new social groups and making important decisions regarding their human capital formation.

Third, we estimate the college friend effect along quantity and quality dimensions, which

provides rich insights into the nature of the estimated effect. Several mechanisms may generate

our observed effects, including joint production, social pressure, or mutual insurance among

network members (Lavy and Sand, 2018). Although we cannot provide a definitive answer as to

the mechanism underlying our estimates, we find some evidence consistent with the joint

production and social pressure explanations.

7 Stinebrickner and Stinebrickner (2006) find relatively small and positive peer effects on grades for women but not

men. Zimmerman (2003) and Sacerdote (2001) estimate positive peer effects on GPA and take-up of social groups

such as fraternities and sororities. Foster (2006) does not find evidence of peer effects.

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2 Data

2.1 Description of the University and Student Outcomes

We use administrative data from Western Washington University (WWU), a regional,

comprehensive university located in Bellingham, Washington with fall undergraduate enrollment

of approximately 15,000 students. In the fall of 2017, WWU enrolled 3,078 freshmen from 37

states and 8 countries. WWU is annually ranked among the top five regional, comprehensive

universities in the U.S. News and World Report rankings.

WWU operates three quarters during the academic year. In each quarter, instruction lasts

for ten weeks, with an eleventh week set aside for final exams. It also operates an optional

summer quarter with about one-fourth of its regular enrollment. Because both housing and dining

options change significantly in the summer, we exclude these quarters from our analysis. WWU

takes pride in offering small instructional experiences and often splits courses into several

sections taught by individual instructors. For example, during a quarter there are often five or six

stand-alone sections of Introduction to Microeconomics taught by two or three instructors.

Across the university, the average section size is 15.8 students and the median section enrolls 11

students.

Using unique student identification (ID) numbers, we merge data from the university

dining halls with administrative records us to observe each student’s background prior to

enrolling in WWU (high school GPA, high school attended, SAT scores) as well as students’

academic records while at WWU (the courses attempted and grades earned in those courses).

We have complete data from five academic years, starting in 2013-2014 and ending in 2017-

2018. Although we have academic records for every undergraduate enrolled at the university, we

restrict our analysis to freshmen, since freshmen at WWU overwhelmingly live on campus and

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use the university dining halls.8 After their freshmen year, students frequently move off campus

and are much less likely to eat in the dining halls. Because we cannot identify friendships among

these students, we do not include advanced undergraduates in our analytic sample.

Panel A of Table 1 presents descriptive statistics of 14,281 freshmen who make up the

analytic sample employed in this paper. Importantly, 86% of the sample are observed to dine on

campus each quarter during their freshmen year while only 9% of freshmen are never observed

in the dining halls. The average SAT score of the analytic sample is 1124, and about one-third of

freshmen are first-generation college students meaning neither of their parents graduated from a

four-year college. Finally, the majority of students are white and almost three-fifths are women.

WWU’s campus housing is served by three dining facilities. Students may eat at any

dining hall of their choice and dining halls remain open throughout the day. There are four

different meal plans available for purchase, respectively offering 80, 100, 125, or an unlimited

number of meals per quarter. Meal plans are purchased quarterly with many students changing

their plan from one quarter to the next. Panel B of Table 1 shows that the 125-meal plan is the

most common choice for freshmen, with the unlimited meal plan being the next most popular.

Food is provided on an all-you-can-eat basis in the dining hall. Most students who live on

campus are required to purchase a meal plan. 9

Our empirical goal is to understand how the presence of friends in a class impacts a

student’s grades. WWU assigns letter grades (grade points) of A (4), B (3), C (2), D (1), and F

(0). In addition, grades can be assigned a plus or minus where grade points are adjusted

8 WWU uses the term freshmen to refer to students enrolling at WWU with no intervening educational experience

between high school and WWU. This includes students who may have participated in a dual enrollment program

while enrolled in high school, but excludes students who attended a different degree-granting institution after high

school graduation. 9 Meal plans are not required for students who live in one of two buildings where housing includes kitchens. These

buildings contain 544 out of 4040 total beds on campus and are usually populated by upper classman rather than

freshmen.

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downwards by three-tenths of a point if a minus is assigned and upwards by the same amount on

all letter grades except an A which cannot receive a plus. Panel C of Table 1 shows that the

average freshmen grade is 2.91 with a standard deviation of 1.01. Although we will express our

results in terms of grade points, note that since the standard deviation is nearly one, we could

state them equivalently in terms of standard deviations. This facilitates comparison of our

findings with the wider literature on academic performance. Panel C also highlights the other

control variables used in our empirical specifications. Students are asked to list academic areas

of interest on their application for admission (class in interest). Ten percent of classes taken by

freshmen are in one of those areas of interest. In order to control for knowledge of a subject, we

sum the prior credits earned in the department in which the student’s current course is offered

(prior department credits). 10 On average, students have taken 1.05 prior credits in this

department. Finally, using the definition of friendship developed in the next section, 14% of

students have a friendship in a class, and 53% take at least one class with a friend during their

freshmen year.

2.2 Description of Friendship Measures

Students obtain access to WWU’s dining halls after an attendant swipes the meal plan

holder’s university identification card through a card reader. The card reader records the meal

plan holder’s unique ID number, the location, and the date and time (measured to the second) of

each swipe. We refer to any student observed entering the dining hall on one or more occasions

in a quarter as a “diner” in that quarter.

Table 2 displays information concerning the frequency of dining hall use among all

freshmen who have a meal plan. The median freshman visits the dining hall 90 times per

10 Classes at WWU are assigned one credit for each hour per week of instruction, and for every two hours per week

of laboratory or rehearsal.

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quarter. With 77 days in an 11 week quarter, this implies that most students eat in the dining hall

at least once per day. Roughly three quarters of students eat at least 60 meals in the dining hall

per quarter, or about five meals per week. Twenty-six percent of students purchase unlimited

access to the dining hall, and as we would expect, these students eat at the dining hall much more

often than those on a fixed-number meal plan.

We exploit the dining hall data to identify members of each student’s social network. We

infer that a social relationship exists between any two students who frequently enter the dining

hall together. Accordingly, to designate two students as friends, we specify a time window, or

alternatively “time bandwidth”, and define a “meeting” as any occasion when the students enter

the dining hall within that window. We specify a meetings threshold, and consider two students

to be friends in a quarter when they meet at least that threshold number of occasions.

Table 3 illustrates the prevalence of friendships using alternate designating criteria. Data

in the table are the averages across quarters, rounded to the nearest whole number. For example,

in the average quarter, there are 6,059 pairs of freshmen who entered the dining hall within 30

seconds of each other on ten or more occasions. We observe a small number of pairs who meet

extremely often – for instance, there are 163 pairs of friends who enter the dining hall within 30

seconds of each other at least 75 times – about once per day – each quarter.

To explore the role of friends on academic outcomes, we focus on time bandwidths and

meeting thresholds of 30 seconds and 10 meetings, respectively. That is, our default criteria are

that two students must enter the same dining hall within 30 seconds of each other at least 10

times within a quarter to be designated as friends in that quarter. As we show in Section 5, our

results are generally not sensitive to these specifications. Using these default criteria, Table 4

shows the frequency of observed friends in our five-year sample. Table 4 includes all freshmen

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and designates those without a meal plan as having zero friends, a possible source of

measurement error to which we return later. Table 4 shows that 80% of fall quarter freshmen

have at least one friend. This number falls slightly as the academic year progresses, most likely

because students tend to use the dining hall less later in the year.

Research on friendships frequently emphasizes homophily, or the tendency for

friendships to form between people who are similar to each other in some respect.11 For

instance, homophily has been shown to be prevalent along racial and ethnic dimensions, gender,

age, behavior, and occupational interest.12 To validate our method for designating friendships,

Table 5 shows that pairs of freshmen diners identified as friends are exceptionally similar across

a range of observable characteristics relative to random pairings of students. Friends are

particularly more likely to be of the same gender, to have attended the same high school, and to

have reported an interest in majoring in the same department upon enrollment (same interest).

Table 5 also indicates that friends are more likely to have a similar demographic and

socioeconomic background, using first-generation status as a proxy for the latter.13 This, along

with the improbability of repeatedly entering a dining hall with the same stranger, provides

evidence that pairs of students we identify as friends indeed have a social relationship.

Recall that our research focus is to assess the effect of friends on academic performance

in a class. In Table 1, we saw that 53% of freshmen enroll in at least one class with a friend over

the academic year. Table 6 gives more detailed information about how frequently students taking

classes with friends identified in the dining hall data. During the average fall quarter, 72% of

freshmen have no observed friends in any of their classes. About one-in-five freshmen take one

11 See Block and Grund, (2014). 12 See Goodreau, et al. (2009), Smith-Lovin and McPherson (1993), Fischer (1977), Knecht, et al. (2010), and

Kalmijn (1998) for evidence of homophily across each of these dimensions, respectively. 13 Recall that first-generation students are defined as those whose parents did not complete a university degree.

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class with a friend and a small number of students have friends in multiple classes. As the

academic year progresses, students are observed taking slightly more courses with friends—

about one-third of students have at least one class with a friend during the winter and spring

quarters.

3 Empirical Model and Identification Strategy

3.1 Empirical model

To estimate the effect of having a friend in a class, we start with a basic econometric

model of student-course grade performance, 𝑌𝑖𝑘𝑠𝑡, with student-level controls of the form:

(1) 𝑌𝑖𝑘𝑠𝑡 = 𝛼 + 𝛽𝐹𝑟𝑖𝑒𝑛𝑑𝑖𝑘𝑠𝑡 + 𝑿𝑖𝑘𝑠𝑡′ 𝛾 + 휀𝑖𝑘𝑠𝑡

where students are indexed by i, courses by k, course-sections (i.e., instructor-by-meeting time)

by s, and quarter by t.14 The variable Friendikst is an indicator variable that takes the value one if

student i has a friend in course k, section s during quarter t. The parameter of interest is 𝛽 which

measures the academic performance of a student with a friend in class relative to performance

when a friend is not present. In some specifications we allow the effect of friends on

performance to vary by the number of friends within a class. To do this, we define another binary

variable, multiple friends, which indicates whether there is more than one friend in a class. In

equation (1), 𝛼 is a constant and 휀𝑖𝑘𝑠𝑡 is a stochastic error term clustered at the class level.15

The vector 𝑿𝑖𝑘𝑠𝑡 contains student-level characteristics designed to capture effort

(attempted number of credits within the quarter), ability (SAT score), and the likely amount of

14 Quarters included are Fall, Winter, and Spring from Fall 2013 to Spring 2018. 15 We follow Lavy and Sand (2018) and cluster the standard errors at the class level. Clustering at the student,

instructor, course, or quarter level produces very similar standard errors.

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enthusiasm the student has for the class measured by class in interest and prior department

credits.

To arrive at our preferred econometric specification, we include student and class-section

fixed effects, 𝛼𝑖 and 𝛿𝑘𝑠𝑡, which necessitate dropping the SAT score which is collinear with the

student fixed effects. Our preferred model can thus be represented as:

(2) 𝑌𝑖𝑐 = 𝛼𝑖 + 𝛽𝐹𝑟𝑖𝑒𝑛𝑑𝑖𝑐 + 𝑿𝑖𝑐′ 𝛾 + 𝛿𝑐 + 휀𝑖𝑐

where the combination of indices k, s, and t have been replaced by the single class-section index

c. This within-student and within-class model identifies 𝛽 by comparing a student’s relative

performance in classes taken with one or more friends to the student’s relative performance in

other classes.

3.2 Identification

In this section, we address three potential sources of bias: omitted variables, simultaneity,

and measurement error.

3.2.a Omitted Variables

The inclusion of the fixed effects in equation (2) help address many omitted-variable

threats to obtaining unbiased estimates of 𝛽 using ordinary least squares (OLS). Employing

classroom fixed effects implicitly controls for course fixed effects and instructor fixed effects,

which, in turn, controls for the possibility that students and their friends select into relatively

easy courses or instructors. Additionally, classroom fixed effects have the advantage of

standardizing grades across classes as students’ grades are relative to the average grade within

each class. We include student fixed effects to allow a student’s performance in classes taken

without friends to serve as a counterfactual for grades in classes taken with friends present. This

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ensures that our results are not driven by time-invariant unobserved characteristics of those

students who have friends or choose to take classes with friends. For example, if better students

are more likely to take classes with friends, omitting the student-level fixed effect would lead

researchers to erroneously conclude that friends are associated with higher grades—a positive

bias of 𝛽 in our specification.16

While fixed effects address many threats to validity, we are careful to address further

identification issues stemming from omitted variables. For example, students’ dedication to

college may vary across quarters. When students are more dedicated, they may earn higher

grades and use the dining hall more often, and thus have more observed friendships.17

Alternatively, students may earn higher grades in courses in which they have an affinity and may

be more likely to form friends in these courses. We address the first issue by controlling for

attempted credits, which measure the number of credits a student registers for at the beginning of

the quarter. To the extent that attempted credits measure dedication to college, the inclusion of

this variable reduces potential omitted variable bias. To address the issue of subject-specific

interest driving both higher grades and observed friendships, we include controls for both stated

academic interest (measured at the department-level and revealed by students on their application

for admission) and revealed interest in the course’s department as measured by department-

specific accumulated credits at the beginning of the quarter.18

16 Since friendship is a function of dining hall use, the student fixed effect also controls for the possibility that

students who use the dining hall more often, and thus are observed having more friends, are fundamentally different

from students who use the dining hall less often. 17 Note that any time-invariant component of student dedication is captured by the student fixed effects 18 We find some evidence that students with a friend in class are actually slightly less likely to be enrolled in a class

that matches their stated interested. A linear probability model with student and classroom fixed effects suggests that

the presence of a friend reduces the likelihood that the course is in the student’s program of interest by 0.4

percentage points (p-value = 0.067). Since roughly ten percent of student-course observations are in the student’s

program of interest, this represents about a four percent decrease.

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To resolve any remaining concerns about endogeneity induced by time-varying student

characteristics, we also report results from a specification that include a student-by-quarter fixed

effect. This specification identifies the friend effect using grades earned in classes taken with

friends relative to classes without friends taken by the same student in the same quarter. This

identification strategy has the limitation in that the friend effect is only identified for students

who have classes both with and without friends during the same academic quarter. It also

precludes the use of attempted credits as an explanatory variable since this does not vary within

quarter.

The estimated friend effect from equation (2) may remain biased if some other

unobserved factor affects both the likelihood of having a friend in class and student performance.

For instance, if subject-specific enthusiasm is not well captured by prior department credits or

stated interest, then friends may tend to be present in those classes that a student would do well

in regardless. If this is driving the measured friend effect, then it follows that we should also

observe higher grades when friends enroll in a different section of same course, including

sections taught by a different instructor. We test for friend effects across both sections and

instructors of a course in Section 5.

3.2.b Simultaneity

If strong class performance foster friendships among classmates, then OLS estimates of

the friend effect will be biased upwards. We address this problem by observing the timing of

friendship formation. Specifically, we estimate the friendship effect for friendship dyads that

were observed to form prior to enrolling in a course together. On the hypothesis that future

course grades do not impact prior friendship development, this approach eliminates simultaneity

concerns in our estimates.

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3.2.c Measurement error

Recall that friendships are determined by two criteria from the dining data: a time

bandwidth to determine whether a meeting occurred and a meeting threshold to determine

whether a pair is designated as friendship. This raises two potential sources of measurement

error. First, 9% of freshmen do not use the dining hall and thus are assigned zero friends. As

demonstrated in the Appendix, our results are essentially unchanged when we drop these

students from our analysis. Second, if the criteria for identifying friendships are either too

restrictive or too permissive, a downward bias will be introduced into any estimate of a positive

friend effect. To see this, it is convenient to describe taking a class with a friend as a “treatment”.

Criteria that are too restrictive will filter out friendships, incorrectly placing treated observations

into the control group, causing the observed differences between the control and treated groups

to be smaller. Criteria that are too permissive will incorrectly identify some observations as

treated and assign friendships to pairs who just happen to dine at similar times and locations.

Again, this will lead to an estimated difference between the treatment and control group that is

too small because non-friends are captured in the treatment group. While there is no obvious

“right” criteria for designating friendships, we show in Section 5 that our results are robust to a

wide range of criteria.

4 Results

4.1 Main results

We estimate equations (1) and (2) by ordinary least squares, clustering the standard errors

at the class level. Table 7 presents the regression results for the entire sample of freshmen,

including those who never use the dining hall and are assigned zero friends. The first column of

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Table 7 presents estimates the coefficients in equation (1), which replaces both the student- and

class fixed effects with students’ combined math and verbal SAT score. According to these

results, having at least one friend in class raises grades by 0.161 grade points, about one-half of

the difference between a B and B+ and roughly equivalent to increasing SAT scores by 110

points (=100×.161/.146). The second column of Table 7 adds the class fixed effects and the third

column includes student fixed effects (and removes the collinear SAT scores). 19 The addition of

each fixed effect reduces the friend effect by about 10%. We simultaneously include both student

and class fixed effects in our preferred model from equation (2) in column 4, and find that the

presence of a friend raises grades by 0.116 grade points.

To test whether the friend effect is increasing with the number of friends in class, column

5 of Table 7 includes the variable multiple friends. Recall that this is a binary variable equal to

one if a student has more than one friend in a class. A student in such a position will have values

of unity for both friend and multiple friend. The associated coefficient of 0.79 suggests that

additional friends have an additional positive impact on grades, though not as large as the initial

impact of the first friend in a class, who raises grades by 0.102 grade points.

The final column of Table 7 replaces student fixed effects with student-by-quarter fixed

effects, and drops the collinear variable attempted credits. The result is similar to our preferred

specification: friends positively impact grades by slightly more than one-tenth of a grade point.

The similarity between this coefficient and that in our preferred specification suggests that there

is little concern about any endogenous selection of friends based upon unobserved student

characteristics that vary from quarter-to-quarter.

19 The sample size changes slightly from column to column for two reasons. First, a small fraction of students are

exempt from the requirement to report SAT scores and are dropped from specifications (1) and (2). Second,

singleton observations that are collinear with the fixed effects are dropped. Estimates from a consistent sample

across specifications are nearly identical to those presented in Table 7 and are available upon request.

19

In Table 7, the other estimated coefficients are consistent with expectations. Students

perform better in classes that are within their interests. The coefficient on attempted credits is

negative in specifications that include a student fixed effect, and positive otherwise, suggesting

that while better students enroll in more credits, individual students get lower grades in quarters

when they attempt more credits than their typical enrollment. The coefficient on prior

department credits is positive in specifications that include the class fixed effect. As students

take more classes in a department, they gain department experience and field-specific knowledge

and perform better. Unsurprisingly, grades are higher in courses in which students expressed an

interest.

To understand how the estimated impact of having a friend in class in Table 7 affects the

distribution of grades, we estimate linear probability models with different letter grades as the

outcome using our preferred specification in equation (2). Table 8 presents the results of four

regressions estimating the probability of an A grade in first column, B grade in the second

column, C grade in the third column, and D or F grade in the last column. The results indicate

that friends in class increase the probability of A grades by 3.6 percentage points and decrease

the probability of C grades and D/F grades by 1.6 percentage points and 2.4 percentage points,

respectively. Relative to the sample means for grade category, these represent relatively large

shifts at the top and bottom of the grade distribution: A grades increase by 10.4% (0.036/0.345)

and D/F grades decrease by 26.1% (0.024/0.092).

4.2 Further exploration

Several natural follow-up questions arise from our central finding that friends in class

have a strong, positive influence on grades. For instance, how does effect vary by characteristics

of either the student or their friend? Perhaps more importantly, through what mechanism exactly

20

do friends exert their positive influence? Although we are unable provide a definitive answer to

the last question, answers to the question about variation in friend characteristics provide some

insight.

Students may benefit more from different types of friends. For example, the friend effect

may be either stronger or weaker when two friends are of the same gender. We also might expect

people to benefit more from either stronger friends or abler friends, where stronger friends share

a tighter social bond, and abler friends have a higher level of academic talent.

To investigate heterogeneity in the friend effect across some characteristic Ω we estimate

a modified version of equation (2) of the form:

(3) 𝑌𝑖𝑐 = 𝛼𝑖 + 𝛽1𝐹𝑟𝑖𝑒𝑛𝑑𝑊𝑖𝑡ℎΩ𝑖𝑐 + 𝛽2𝐹𝑟𝑖𝑒𝑛𝑑𝑊𝑖𝑡ℎ𝑜𝑢𝑡Ω𝑖𝑐 + 𝑿𝑖𝑐′ 𝛾 + 𝛿𝑐 + 휀𝑖𝑐

Where FriendWithΩic is a dummy variable set equal to one if any of student 𝑖’s friends in class 𝑐

have characteristic Ω, and FriendWithoutΩic is defined similarly. We estimate equation (3) using

five different characteristics: opposite gender, high SAT score, low SAT score, first generation,

and strong friend. The first of these indicates whether the student has an opposite gender friend

in class. The second and third are included to measure the effect of more and less able friends,

and respectively indicate whether a friend in class reported an SAT score in the top 75th and

bottom 25th percentiles among all freshmen in our data. The fourth characteristic, first

generation, identifies friends whose parents never obtained a four year post-secondary degree

and is our proxy for socioeconomic background. The final characteristic, strong friend, is set

equal to one if the student and a classmate met together at least 20 times in the dining hall while

enrolled in the course together.

There may also be heterogeneity in the friend effect across types of friendships, rather

than across types of friends. For example, some people may benefit more from a high-ability

21

friend than others. Alternatively, friends may only be helpful if they are not too dissimilar in

terms of ability or socioeconomic background. Furthermore, the differential effect of opposite

gender friends or strong friends may vary by gender. To determine whether there is

heterogeneity in grade improvement by friendship type, we estimate equation (3) using both our

analytical sample (all freshmen), and for samples restricted by gender, ability, and

socioeconomic background.

Table 9 presents OLS estimates of the coefficients 𝛽1 and 𝛽2 from equation (3) for our

analytical sample and for the restricted samples. The last column of the table displays the

difference between the coefficients, and indicates whether that difference is statistically

significant according to a Wald test. Before turning to each characteristic, note that the

coefficients 𝛽1 and 𝛽2 are positive and significantly different from zero throughout Table 9,

suggesting that friends have a positive effect on grades regardless of the characteristic under

consideration.

As an aid to understanding Table 9, consider the first panel which focuses on opposite

gender friends. Under the complete sample (analytic), the effect of having a friend of opposite

gender is .106 which is identical to the effect of a friend without that characteristic (i.e., a friend

of the same gender). When the sample is restricted to men, the effect of an opposite gender

friend is .153 which is slightly higher, though not statistically different, than the effect of a same

gender friend (.128). Likewise, when the sample is restricted to women, there is no statistical

difference in the friend effect if the friend is a man or woman. Interestingly, both coefficients in

the sample of men are higher than those in the sample of women suggesting that male college

students may benefit more from the presence of a friend than a woman does.

22

Table 9 explores the friend effect by academic ability define as being in the upper 25th

percentile of the SAT (High SAT Score) or the lower 25th percentile (Low SAT Score). As the

high SAT panel demonstrates, the impact of making a high ability friend is similar to the impact

of making friends that aren’t high ability, and this is true across different sample restrictions.

However, in the Low SAT Score panel, the benefit gained from making a low ability friend is

smaller than the benefit of making a friend who is not low ability for all students. Moreover, this

differential effect appears to be decreasing in ability: for students in the bottom quartile of the

SAT distribution, a friend in the bottom quartile has a much smaller positive impact on grades

(.063) than a friend outside of this quartile (.140). Students in the top quartile, however, seem to

benefit uniformly regardless of their friends’ ability.20

Table 9 also shows that first generation college students (defined as students whose

parents didn’t finish college) benefit more from non-first generation friends. Non-first generation

students however, do not receive a significantly reduced benefit from a first generation friend.

These results are in line with Lavy and Sand (2018), who find that friends with parents with

higher levels of education have a greater positive impact than friends whose parents have lower

levels of educational attainment.

The last panel of Table 9 show that for women, the friend effect on grades is increasing in

the strength of friendship (defined as friends who meet more than 20 times in the dining hall).

This may be indicative of differences in social relationships across genders. For example, if

women dine more often with diverse companions, a higher meetings threshold may be necessary

to identify friendships strong enough to enhance class performance. We will discuss the

20 A possible policy implication would be for instructors to pair low ability students with high ones, for the benefit

of both less able students, and mid-range students who are preferentially paired together. However, these results may

only extend to chosen friendships rather than random pairings of students.

23

relationship between the effect size and friendship strength in more detail in Section 5. A more

thorough exploration of friendship formation across genders is left for later research.

As a second method of exploring heterogeneity, Table 10 provides estimates of the

friendship effect by class characteristics. We examine two class characteristics: size and

difficulty. A class is considered large if it enrolls at least 45 students and difficult if the class

GPA among students without friends is less than 2.9.21 The results from including an interaction

between indicators for each of these groups and the friend indicator from equation (2) is given in

columns 2 and 3 of Table 10. The estimate of the friendship effect from column 4 of Table 7 is

provided in column 1 for reference. The point estimates indicates that friends have a significantly

greater impact in larger classes but no differential effect in more difficult classes, perhaps

suggesting a mechanism through which friends improve grades is through mutual instruction (if

time with an instructor is harder to come by in larger classes).

Though the estimation output is not presented here, we further investigate mechanisms

behind the friend effect by determining whether academic performance decreases in non-friend

classes during the same quarter when a friend is present in at least one class. If so, it would

suggest substitution from classes without friends to those with friends. To do this, we create an

indicator that takes the value one if a friend is present in another class in the same quarter. We

add this friend-in-other-class indicator to equation (2) and drop the friend-in-class indicator. We

find that grades do not significantly change in non-friend classes. If effort is zero-sum across

class, this suggests that having a friend in class may lead to increases in productivity (i.e., joint

productivity). If effort is not zero-sum, then having a friend may increase effort, which may

occur because the returns to productivity have increased (joint productivity) or because friends

21 These group designations were chosen to roughly equalize the number of student-course observations in each

group.

24

decrease the marginal cost of effort if, for example, friends create incentives to compete or

increase enthusiasm (i.e., social pressure in a network environment).

5 Robustness Checks

A natural interpretation of the results in Table 7 is that students learn more when they

have social connections among their classmates. In this section, we exploit the unique features of

our data to show that this interpretation is quite robust. We first show that our results are

insensitive to the criteria for assigning friendships. We next provide a detailed discussion of

possible sources of bias and run several robustness tests exploring these. Our robustness checks

mitigate concerns about omitted variables, simultaneity, and measurement error, and also

strongly suggest that better friends have a larger positive impact on grades.

To obtain the results in Table 7, we designated two students as friends when they enter a

dining hall within thirty seconds of each other at least ten times during a quarter. In Figure 1, we

plot estimates of the friend coefficient from our preferred specification using alternate time

bandwidths and meeting thresholds. Specifically, we illustrate the friend effect using 5-, 10-, 30-,

and 60- second time bandwidths, and meeting thresholds ranging from 1 to 40. Figure 1 shows

that we observe a significantly large and positive friend effect using any reasonable criterion for

designating students as friends.

Figure 1 also shows that as the meetings threshold increases, the observed friend effect

increases and is simultaneously measured less precisely. Under the reasonable assumption that

people who meet more often are better friends, this implies that stronger friends have a larger

impact on course performance. The estimated standard errors increase because fewer

25

observations pass through the higher threshold and we therefore measure the friend effect with

less precision.

An alternative way to assess social connections among classmates would be to dispense

with the meetings threshold entirely. Although friendship is binary in our analysis, in real life it

potentially exists along a continuum. Consequently, it may be appropriate to replace the binary

variable friend with an alternate measure of social interaction with all classmates. To do this, we

construct a new variable that measures the total number of dining hall meetings that each student

has with their classmates. We then replace the binary variable friend in equation (2) with a

quartic in this measure. Because it is difficult to interpret high-order polynomials, we display the

predicted grades (in grade points) in Figure 2. Predicated grades are calculated at the mean

values of the regressors in 𝑿𝑖𝑐′ in equation (2), for zero to 100 meetings with classmates. Note

that the graph is increasing and concave indicating that while grades increase when students have

more social ties with their classmates, this effect exhibits diminishing marginal returns.

We now address potential bias in estimates of β1. As described in Section 3.2.b, we

address simultaneously by leveraging information in the data about the timing of friendships.

More formally, to rule out simultaneity, we introduce three new measures of friendships. The

first, old friend indicates that a dyad formed a friendship in at least one past quarter and this

friendship continued in the current quarter. Past friend identifies pairs of individuals who were

friends in the past, but are not identified as friends in the current quarter. Finally, new friend is a

binary variable that identifies contemporary friendships among pairs of individuals who were not

identified as friends in prior quarters. We include new friend because we need to control for

current friends in class in order to assess the impact of previously formed friends. Because old

friend and past friend rely on observing friends in prior quarters, we drop observations from

26

students’ first quarter on campus. We return to our preferred specification of 10 meetings and 30

seconds for identifying these three new variables.

Table 11 presents estimates of the coefficients on these alternative indicators of

friendship. According to these results, friends made prior to co-enrollment have a positive impact

on grades. Grades are 0.065 points higher if at least one classmate was a prior friend, and 0.115

points higher if a friendship made earlier persists while co-enrolled. This resolves concerns that

the measured friend effect is entirely a product of reverse causality as one does not expect future

course grades to impact previous dining hall choices. Note also that grades are 0.082 points

higher if a friendship is first observed when two students are classmates. Contemporaneous

friends thus have a stronger impact on grades than past friends, but a weaker impact than

longstanding old friends. The most natural interpretation is that friends exert a positive influence

on grades, and closer friends have a stronger influence.

To rule out omitted variable bias, we would ideally use an instrumental variables

approach. Unfortunately, it is difficult to devise an instrument for friend that is uncorrelated with

grades. Fortunately, WWU’s scheduling practices provide us with an alternate way to alleviate

some concerns about endogeneity. Since enrollment in most lectures is capped, WWU offers

multiple sections per quarter of many introductory courses and core major requirements.

Different sections usually meet at different times, but are often taught by the same instructor. For

example, in the fall of 2019, five instructors taught eight sections of Principles of

Microeconomics, three of whom taught two sections each. If friends happen to do well in similar

classes, then we should observe a positive effect on grades when friends are enrolled in different

sections of the same course.

27

Accordingly, Table 12 presents estimates of the friend effect across class sections.

Specifically, the table presents results from two regressions. In the first regression, we add the

dummy friend - different section, same instructor to equation (1). This indicates whether the

student has a friend who is taking the same course with the same instructor, but in a section that

meets at different times. In the second regression, we include the variable friend - different

instructor, which is set equal to one if a friend is enrolled in a section of the same course that is

taught by a different instructor. Columns (2) and (3) of Table 12 present estimates of both the

coefficient of interest β1, and the coefficients on the distinctive dummies in the two robustness

regressions. For comparability, column (1) reproduces results from our preferred benchmark

model.

The results in column (2) indicate that friends influence grades when they share an

instructor, but the influence is strongest when friends attend class together. A student’s expected

grade is 0.075 grade points higher when a friend is enrolled in the same course with the same

instructor, but at a different time. With a friend enrolled in the same section, the friend effect is

0.117 grade points, or about 55%, stronger. The results in column (3) show that students do not

receive any benefit when friends take the same course with a different instructor - the coefficient

on friend - different instructor is near zero and insignificant.

These results provide evidence that the observed friend effect is not the spurious

consequence of an unobserved omitted variable. This is because under most reasonable

endogeneity stories involving an omitted variable, we would expect to see an effect across

instructors of the same course. If friends have no effect on grades, then grades must be higher in

classes taken with friends for some other reason. The most logical external quantity that would

boost the grade of two friends in a course is shared interest or affinity for the subject matter that

28

is not captured by our department-level controls for interest. In other words, people may

preferentially befriend others who will turn out to enjoy and do well similar material. Since the

same course generally covers the same material regardless of instructor, we would then observe a

positive effect when friends take the same course with a different instructor.

It is more challenging to concoct an endogeneity story consistent with the results of Table

12. If friends do not affect grades, then we would need to explain both why grades are higher in

classes taken with friends, and why this impact is largest when the friends share their instructor

in the same classroom at the time. To us, the most logical interpretation of Table 12 is that

through some mechanism, friends have a positive impact on grades. A weaker version of the

same mechanism may explain the positive coefficient on friend - different class, same

instructor. For example, friends may help each other understand the same instructor’s course

materials, but collaboration is easier when they attend class at the same time and share a memory

of the same lecture.

A final concern with our approach has to do with the potential undercounting of

friendships. Our sample of freshmen introduces this possibility. Specifically, our approach

utilizes all freshmen observations, including those who do not live on campus and, hence, who

do not have dining hall privileges. Because these individuals are never observed entering the

dining hall, they are assigned zero friends. However, these individuals likely form unobserved

friendships and, in the terminology of treatment and control groups, are incorrectly assigned to

the control group. This problem is mitigated somewhat by the fact that 86% of freshmen

observations eat in the dining hall each quarter, and so the number of false zeros is likely small.

To address this issue, recall that we estimated all regressions from Table 7 in Appendix Table 2,

but excluded from the sample all freshmen without a dining hall plan. Using our preferred

29

specification, a friend in class raises GPA by .115 points, almost identical to that reported in

Table 7.

6 Conclusions

Using a revealed-preference based method of determining friendships, this paper

documents that students who take college-level courses with friends earn significantly higher

grades than they do when enrolled in courses without friends. This increase in grades is

significant both statistically and practically, with the impact on grades being about one-half of

the difference between an A- and an A, or equivalently, about the same magnitude as increasing

a student’s SAT score by about 100 points. This effect occurs in the presence of student-,

course-, and student-quarter fixed effects suggesting that these results are not driven by

unobservables that remain unchanged within a student, within a quarter, or within a course. This

effect grows in the strength of friendship (measured by the number of dining hall meetings) and

the number of friends in a course. The friend effect is also present for friendships that were

formed prior to course enrollment indicating that these results are not driven by the simultaneous

formation of friendships and academic performance. Further, the effect of having a friend in the

same course taught by a different professor is statistically no different than zero implying that

our measure of friendship does not serve as a proxy for shared enthusiasm for a subject.

Moreover, there are reasons to believe that we have understated the true friendship effect. For

instance, we document that enrolling in a class with a friend reduces a student’s likelihood of

dropping the course or of earning a D or F. Under these circumstances, friendships may also

reduce the time and costs of earning a degree. Taken as a whole, it appears that friendships play

an important role in academic achievement and, through that, in human capital formation.

30

As pointed out in the introduction, there is a vast literature on peer effects and their role

in academic achievement. However, the literature on friendships is more sparse, partly because

of its reliance on self-reported friendship data. In addition, the analysis of friendship in the

academic literature has been limited to elementary and secondary aged children. Ours is the first

to document the role of friendships on academic outcomes among college aged adults. As might

be expected, there are similarities and differences between the extant literature and our findings.

For instance, Lavy and Sand (2018) find that the education level of a friend’s parents has a

positive impact on academic achievement among middle school students, a similar finding to that

presented in this paper which shows a larger academic effect when a friend comes from a family

whose parents completed a college education. When examining high school students, Hill

(2015) finds that opposite gender friends decrease own GPAs which stands in marked contrast to

our findings that both same and opposite gender friends have a consistent positive effect on

grades.

One open question in this research has to do with the mechanism by which friendship

leads to higher grades. Certainly one can imagine friends aiding and encouraging each other, by

serving as insurance for each other in case one misses course material, or by eliciting more effort

from an individual. While we cannot identify the specific mechanism, having a friend in one

class does appear to decrease grades in other classes thus ruling out mechanisms that involve

substituting effort or resources between classes.

Given that friends are strongly associated with better grades, it is worth commenting on

policies that might encourage friendships. Universities have long created structures and

programs to increase social interactions among their students. Indeed, WWU has a number of

programs that encourage friendships even before students set foot on campus in the fall as well

31

as social events that take place in residence halls throughout the year. Further, faculty can create

class environments that encourage social interaction. To the extent that these programs enable

friendships to form, they may have indirect academic benefits that outweigh their costs. Of

course universities are also expanding programs in which it is difficult to have friendship

support—most notably the role of online courses. Our read of the online course literature

suggests that academic outcomes in these courses tend to be lower than face-to-face courses

possibly as a result of less meaningful social interactions between students in online courses.

32

Table 1 Descriptive Statistics for the Analytical Sample

Mean

Standard

deviation

Number of

observations

Panel A: Student-Level Data fraction who dine every quarter 0.86 0.35 14,281

fraction who never dine 0.09 0.29 14,281

fraction who take at least one class with a friend 0.53 0.50 14,281

fraction male 0.42 0.49 14,280

fraction white 0.73 0.44 14,281

fraction black 0.04 0.19 14,281

fraction hispanic 0.08 0.27 14,281

fraction first generation 0.31 0.46 14,281

SAT score 1124 148 14,250

Panel B: Student by Quarter-Level Data

fraction who dine 0.89 0.32 40,869

unlimited meal plan 0.26 0.44 40,869

125 meals 0.30 0.46 40,869

100 meals 0.18 0.38 40,869

75 meals 0.15 0.36 40,869

attempted credits 14.67 1.74 40,869

Panel C: Student by Course-Level Data grade 2.91 1.01 127,929

prior department credits 1.05 2.41 128,222

class in interest 0.10 0.30 128,222

friend in class 0.14 0.34 128,222

33

Table 2

Distribution of student dining hall entries

Meal Plan

Percentile Total Unlimited 125 meals 100 meals 75 meals

10th 42 69 52 39 21

25th 65 101 75 60 39

Median 90 135 96 80 57

75th 117 168 113 92 68

90th 157 197 120 97 73

Number of

student-

quarters

36,209 10,662 12,296 7,174 6,077

Table 3

Number of friendships observed among freshmen using various designating criteria, average across

quarters

Time bandwidth (seconds)

Meetings 5 10 30 60

1 44,993 145,484 514,019 918,145

2 8,521 19,058 91,677 253,517

3 5,850 10,560 26,745 83,225

4 4,632 8,479 14,145 34,188

5 3,821 7,281 10,563 18,450

6 3,219 6,402 8,934 12,542

7 2,767 5,748 7,900 9,860

8 2,408 5,217 7,156 8,380

9 2,099 4,757 6,551 7,429

10 1,854 4,370 6,059 6,727

15 1,027 3,000 4,336 4,707

20 613 2,144 3,226 3,494

25 375 1,557 2,453 2,657

30 236 1,145 1,882 2,054

35 148 855 1,440 1,578

40 94 635 1,108 1,219

60 19 191 364 415

75 6 77 163 192

100 1 19 49 65

34

Table 4

Distribution of observed friendships among freshmen

Fall Winter Spring

No. of Friends Count (%) Count (%) Count (%)

0 2823 20 3614 27 4200 32

1 2432 17 2417 18 2555 20

2 2320 16 2145 16 1993 15

3 2079 15 1762 13 1577 12

4 1520 11 1217 9 1074 8

5 1080 8 880 6 624 5

6 720 5 546 4 412 3

7 456 3 386 3 228 2

8 319 2 251 2 207 2

9 187 1 172 1 88 1

10 or more 265 2 209 2 111 1

No. of Students 14,201 13,599 13,069

35

Table 5

Characteristics of friendships and of all pairs of freshmen dining hall users, weighted averages

across academic years.

Fall Winter Spring

friends all pairs friends all pairs friends all pairs

both male 33.6% 17.6% 36.4% 17.9% 36.4% 18.0%

both female 43.3% 33.7% 40.8% 33.2% 40.9% 33.1%

both minority 8.8% 7.4% 8.9% 7.4% 9.3% 7.5%

both white 56.4% 53.0% 57.2% 53.1% 57.8% 52.9%

both black or both Hispanic 1.4% 0.8% 1.4% 0.8% 1.4% 0.8%

both first generation 9.7% 8.9% 9.3% 8.7% 9.2% 8.5%

neither first generation 54.0% 49.3% 53.8% 49.8% 54.6% 50.3%

same high school 19.1% 0.5% 15.4% 0.5% 15.2% 0.5%

same interest 7.3% 4.6% 7.0% 4.6% 7.3% 4.6%

observations 7,373 6,692,518 6,117 5,847,163 4,814 5,100,806

Fall Winter Spring No. of Classes Count (%) Count (%) Count (%)

0 10,269 72 9,158 67 9,213

70 1 2,743 19 2,993 22 2,524 19

2 959 7 1,075 8 948 7

3 213 1 309 2 327 3

4 or more 17 0 64 0 57 0

No. of Students 14,201 13,599 13,069

Table 6

Distribution of classes taken with friends, all freshmen

36

(1) (2) (3) (4) (5) (6)

friend 0.161*** 0.149*** 0.144*** 0.116*** 0.102*** 0.111***

(0.012) (0.008) (0.012) (0.007) (0.008) (0.008)

multiple friends 0.079***

(0.015)

attempted credits 0.049*** 0.038*** -0.006*** -0.008*** -0.008***

(0.002) (0.002) (0.002) (0.002) (0.002)

prior department credits -0.009*** 0.013*** -0.027*** 0.004*** 0.004*** 0.007***

(0.002) (0.002) (0.002) (0.001) (0.001) (0.002)

class in interest 0.225*** 0.063*** 0.151*** 0.090*** 0.090*** 0.080***

(0.012) (0.010) (0.012) (0.009) (0.009) (0.009)

SAT (100s) 0.146*** 0.142***

(0.003) (0.003)

student fixed effect

student-quarter fixed effect

class fixed effect

Observations 127,673 125,671 127,867 125,835 125,835 124,997

𝑅2 0.063 0.318 0.469 0.670 0.670 0.780 Notes: See section 3 for a definition of the independent variables.

*p<0.1, **p<0.05, ***p<0.01

Table 7

Baseline Results, All Freshmen

37

Table 8

Friend Effect on the Grade Distribution

Outcome

A grade B grade C grade D or F grade

friend 0.036*** (0.004)

0.004 (0.005)

-0.016*** (0.004)

-0.024*** (0.002)

Sample mean of

dependent variable

0.345 0.372 0.190 0.092

Observations 126,135 126,135 126,135 126,135

𝑅2 0.553 0.286 0.331 0.435 Notes: The dependent variable is a binary indicator for each grade category. All regression models contain student

and class fixed effects as well as student-quarter level controls for attempted credits and accumulated department

credits and a student-course level binary indicator for whether the course is in the academic department of the

student’s program interest. Standard errors (in parentheses) are corrected for clustering at the class level.

*p<0.1, **p<0.05, ***p<0.01

38

Table 9

Friend effect by friend characteristics

Friend

characteristic

Sample friend effect with characteristic without characteristic with-without

Baseline Analytic 0.116***

(0.007)

Opposite

gender

Analytic 0.106***

(0.013) 0.106***

(0.008) 0.000

Men 0.153***

(0.018) 0.128***

(0.013) 0.025

Women 0.070***

(0.016) 0.084***

(0.009) -0.014

High SAT

Score

Analytic 0.100***

(0.013)

0.110*** (0.008)

-0.011

High SAT 0.089***

(0.021) 0.094***

(0.018) -0.004

Low SAT 0.118***

(0.040) 0.115***

(0.016) 0.003

Low SAT

Score

Analytic 0.075***

(0.012)

0.120*** (0.007)

-0.045***

Low SAT 0.063***

(0.024) 0.140***

(0.017) -0.077***

High SAT 0.087***

(0.039) 0.102***

(0.015) -0.014

First

generation

Analytic 0.083***

(0.011) 0.115***

(0.008) -0.032**

First gen. 0.067***

(0.013) 0.109***

(0.009) -0.042**

Not first gen. 0.121***

(0.020) 0.135***

(0.015) -0.014

Strong (at least 20

meetings)

Analytic 0.121***

(0.008) 0.074***

(0.010) 0.046***

Men 0.136***

(0.014) 0.114***

(0.017) 0.022

Women 0.106***

(0.010) 0.037***

(0.011) 0.069***

Notes: Each row represents a separate regression. All regression models contain student and class fixed effects as

well as student-quarter level controls for attempted credits and accumulated department credits and a student-course

level binary indicator for whether the course is in the academic department of the student’s program interest.

Standard errors (in parentheses) are corrected for clustering at the class level.

*p<0.1, **p<0.05, ***p<0.01

39

Table 10

Friend effect by class characteristics

(1) (2) (3)

friend 0.116*** (0.007)

0.083*** (0.010)

0.122*** (0.010)

friend * (large class) 0.051*** (0.014)

friend * (difficult class) -0.012 (0.014)

Observations

𝑅2

125,835

0.670

125,835

0.670

125,835

0.670

Notes: The dependent variable is the student’s course grade. The large class indicator takes the value one if the class

has at least 45 students and is zero otherwise. The difficult class indicator takes the value one if the class grade point

average is less than 2.9 and is zero otherwise. All regression models contain student and class fixed effects as well

as student-quarter level controls for attempted credits and accumulated department credits and a student-course level

binary indicator for whether the course is in the academic department of the student’s program interest. Standard

errors (in parentheses) are corrected for clustering at the class level.

*p<0.1, **p<0.05, ***p<0.01

Table 11

Friend effect by timing of the friendship

new friend 0.082***

(0.014)

old friend 0.115***

(0.010)

past friend 0.065***

(0.013)

Observations 83,318

𝑅2 0.704

Notes: This single regression contains student and class fixed effects as well as student-quarter level controls for

attempted credits and accumulated department credits and a student-course level binary indicator for whether the

course is in the academic department of the student’s program interest. Each of the friend variables is an indicator

for the following: new friend is a current but not past friend, old friend is a past and current friend, and past friend is

a past but not current friend Standard errors (in parentheses) are corrected for clustering at the class level.

*p<0.1, **p<0.05, ***p<0.01

40

Table 12 Friend effect across instructors and class-sections

(1) (2) (3)

friend 0.116*** (0.007)

0.117*** (0.007)

0.116*** (0.007)

friend – different section, same instructor 0.075*** (0.011)

friend – different instructor 0.004 (0.009)

Observations

𝑅2

125,835

0.670

125,835

0.670

125,835

0.670

Notes: All regression models contain student and class fixed effects as well as student-quarter level controls for

attempted credits and accumulated department credits and a student-course level binary indicator for whether the

course is in the academic department of the student’s program interest. Standard errors (in parentheses) are corrected

for clustering at the class level.

*p<0.1, **p<0.05, ***p<0.01

41

Figure 1

The friend effect according to alternate time and meetings bandwidths.

42

Figure 2

43

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45

Appendix Table 1

Student Counts

2013-2014 2014-2015 2015-2016 2016-2017 2017-2018

F W Sp. F W Sp. F W Sp. F W Sp. F W Sp.

1 UG Enrollment 13,452 12,844 12,149 13,457 12,915 12,284 13,640 13,088 12,564 13,815 13,181 12,479 14,555 13,909 13,114

2 Freshmen 2760 2664 2545 2749 2635 2546 2761 2644 2545 2853 2707 2607 3078 2949 2826

3 Diners 3443 3306 3127 3406 3231 3034 3333 3188 3003 3400 3232 3077 3518 3342 3098

4 Freshmen 2572 2424 2257 2507 2323 2171 2496 2348 2193 2567 2385 2251 2753 2572 2390

5 % Diners 93.2% 91.0% 88.7% 91.2% 88.2% 85.3% 90.4% 88.8% 86.2% 90.0% 88.1% 86.3% 89.4% 87.2% 84.6%

Meal Plan

6 unlimited 874 755 624 869 723 608 793 619 556 773 683 583 870 712 620

7 125 meals 1028 757 640 980 725 578 1030 754 638 1103 741 595 1202 842 683

8 100 meals 484 541 521 470 461 449 462 500 449 493 509 494 414 438 454

9 75 meals 186 371 472 188 414 536 211 475 550 198 452 579 267 545 633

This table shows enrollment and dining hall usage over four academic years at Western Washington University. Enrollment is calculated by

counting the unique id numbers that have completed at least one class for credit in the WWU academic data. Students who do not receive credit for

any class in a quarter are not included.

Row 5 in the table gives the fraction of freshmen who entered a university dining hall in the indicated quarter, and is the ratio of rows 3 and 6.

46

Appendix Table 2 Baseline results, dining hall users

(1) (2) (3) (4) (5) (6)

friend 0.160*** 0.143*** 0.145*** 0.115*** 0.101*** 0.110***

(0.012) (0.009) (0.012) (0.007) (0.008) (0.008)

multiple friends 0.079***

(0.015)

attempted credits 0.047*** 0.036*** -0.006*** -0.010*** -0.010***

(0.002) (0.002) (0.002) (0.002) (0.002)

department credits -0.009*** 0.012*** -0.028*** 0.003*** 0.003*** 0.006***

(0.002) (0.002) (0.002) (0.002) (0.002) (0.002)

interest 0.218*** 0.073*** 0.166*** 0.102*** 0.102*** 0.091***

(0.013) (0.011) (0.013) (0.009) (0.009) (0.010)

SAT 0.144*** 0.141***

(0.003) (0.003)

student fixed effect

student-quarter fixed effect

class fixed effect

Observations 113,944 112,017 113,955 112,011 112,011 111,327

𝑅2 0.062 0.321 0.465 0.670 0.670 0.778